A Sharp Ramsey Theorem for Admissible Colorings of Ordered Cliques

Let \(f(k)\) be the minimum integer \(N\) such that any red--blue edge-coloring of the ordered complete graph on \(N\) vertices contains a set of \(k\) vertices whose induced coloring is admissible.

In this note, we obtain the exact value of $f(k)$ for $k\ge 3$, which confirms a conjecture posed by Bradač, Liu, Wu and Xu.